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We study the equilibrium joining strategies for customers in an M/M/1 queue with working vacations and vacation interruptions. The service rate switches between a low and a high value depending on system dynamics. The server will take a multiple working vacation when the system is empty, during which a low service rate is provided to the arriving customers if any. Upon completion of the first customer’s service, given that the system is not empty, the working vacation will be terminated which means the server comes back and serves the following customers with a higher service rate. Otherwise, if the system is found empty upon completion of the first service, the server will continue his working vacation. Arriving customers may or may not know the state of the server and/or the number of the customers upon arrival, but they have to decide whether to enter the system or balk based on a linear reward-cost structure. We investigate customer behavior according to different levels of information regarding the system state. The equilibrium strategies for the customers are derived and the stationary behavior of the system under these strategies are analyzed. Finally, the effect of different levels of information on equilibrium thresholds and equilibrium entrance probabilities is illustrated by several numerical examples.
Li, Kaili 1 ; Wang, Jinting 1 ; Ren, Yanjia 1 ; Chang, Jingwei 1
@article{RO_2016__50_3_451_0,
author = {Li, Kaili and Wang, Jinting and Ren, Yanjia and Chang, Jingwei},
title = {Equilibrium joining strategies in {M/M/1} {Queues} with working vacation and vacation interruptions},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {451--471},
publisher = {EDP-Sciences},
volume = {50},
number = {3},
year = {2016},
doi = {10.1051/ro/2015027},
zbl = {1350.60096},
mrnumber = {3519327},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2015027/}
}
TY - JOUR AU - Li, Kaili AU - Wang, Jinting AU - Ren, Yanjia AU - Chang, Jingwei TI - Equilibrium joining strategies in M/M/1 Queues with working vacation and vacation interruptions JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2016 SP - 451 EP - 471 VL - 50 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2015027/ DO - 10.1051/ro/2015027 LA - en ID - RO_2016__50_3_451_0 ER -
%0 Journal Article %A Li, Kaili %A Wang, Jinting %A Ren, Yanjia %A Chang, Jingwei %T Equilibrium joining strategies in M/M/1 Queues with working vacation and vacation interruptions %J RAIRO - Operations Research - Recherche Opérationnelle %D 2016 %P 451-471 %V 50 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2015027/ %R 10.1051/ro/2015027 %G en %F RO_2016__50_3_451_0
Li, Kaili; Wang, Jinting; Ren, Yanjia; Chang, Jingwei. Equilibrium joining strategies in M/M/1 Queues with working vacation and vacation interruptions. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 3, pp. 451-471. doi: 10.1051/ro/2015027
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